Locally Bounded Family
A set (also called a family) U of real-valued or complex-valued functions defined on some topological space X is called locally bounded if for any x0 in X there exists a neighborhood A of x0 and a positive number M such that
for all x in A and f in U. In other words, all the functions in the family must be locally bounded, and around each point they need to be bounded by the same constant.
This definition can also be extended to the case when the functions in the family U take values in some metric space, by again replacing the absolute value with the distance function.
Read more about this topic: Local Boundedness
Famous quotes containing the words locally, bounded and/or family:
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